论基础数学工具的创新运用

在建立叶轮机三元流面理论时，吴仲华巧妙地、创造性地提出了全导数型的沿流面方向偏导数的概念和表达式，导出了两类流面气动力学数学模型，不但数学形式简洁，而且具有明晰的物理意义，有利于分析和求解。在吴氏流面理论的启示下，作者不断致力于基础数学工具和概念的推广和创新运用，挖掘并发挥其潜在功能。本文将通过流体力学、传热学以及最优控制论方面的一些实例来综合介绍个人的心得和体会。

On Innovative Utilization of Basic Tools of Mathematical Analysis

In founding the stream-surface theory of 3-D flow in turbomachinery Wu elegantly suggested the new concept and mathematical expressions of the directional partial derivatives (in form of total derivatives) along the stream surface, and the resulted mathematical model of 3-D flow not only takes a very simple form but also possesses apparent physical meaning and in very advantageous for analysis and solution. Just motivated by that, the author has devoted himself for a long time to the innovative utilization of basic tools of mathematical analysis for handling a variety of problems in applied science in order to bring their potential functions into full play. A brief review of the author's results in fluid dynamics, heat transfer and optimal control theory is given herein for reference.